Abstract
Moving heat load problems appear in many manufacturing processes, such as lithography, welding, grinding, and additive manufacturing. The simulation of moving heat load problems by the finite-element method poses several numerical challenges, which may lead to time consuming computations. In this paper, we propose a 2D semi-analytic model in which the problem in two spatial dimensions is decoupled into three problems in one spatial dimension. This decoupling significantly reduces the computational time, but also introduces an additional error. The method is applied to a wafer heating example, in which the computational time is reduced by a factor 10 at the cost of a 4% error in the temperature field.
Highlights
Moving heat load problems occur in many manufacturing processes, such as welding [1,2,3,4,5,6,7,8], grinding [9,10], metal cutting [11,12], laser hardening of metals [13,14], and additive manufacturing [15,16,17,18]
We have introduced a semi-analytic approximation for the calculation of the 2D temperature field resulting from a moving heat load, by decoupling the problem in two spatial dimensions into three problems in one spatial dimension
On fine meshes, this leads to a significant reduction in computational time compared to a conventional 2D Finite Element (FE) analysis
Summary
Moving heat load problems occur in many manufacturing processes, such as welding [1,2,3,4,5,6,7,8], grinding [9,10], metal cutting [11,12], laser hardening of metals [13,14], and additive manufacturing [15,16,17,18]. These schemes prevent spurious oscilations at the cost of an increased discretization error Another problem is that the area in which the heat load is applied is typically small. Veldman et al / International Journal of Heat and Mass Transfer 122 (2018) 128–137 proposed [3,4,17], which lead to significant reduction in computational effort Note that these schemes require some cost for updating the mesh and that the temporal discretization remains challenging, since the adaptive mesh will keep the mesh size near the source small. We propose a novel semi-analytic approximation method to reduce the computational cost of 2D transient moving load problems with constant coefficients.
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